Our objective is to determine the quantitative relationships between the cellular oxygen concentration and the cellular metabolic state. The mitochondria are responsible for most of the cellular oxygen consumption, utilizing the oxygen and cellular reducing power (substrates) to produce the required adenosine triphosphate as the energy supply. A mathematical description of these interrelationships has been developed which will be tested for its ability to fit the mitochondrial behavior both in isolated suspensions and intact cells. This behavior will be tested for a wide range of oxygen concentrations and substrates in order to provide a basis for understanding tissue behavior under low oxygen conditions. The properties and mechanism of the enzyme which directly reacts with molecular oxygen will also be examined in order to understand its central role in the control of the mitochondrial (and, therefore cellular) respiratory rate.